Umklapp scattering in unconventional superconductors: Microwave conductivity shows that $\ensuremath{\kappa}\ensuremath{-}{(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF})}_{2}\mathrm{Cu}[\mathrm{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$ is a ${d}_{xy}$ superconductor

Umklapp scattering in unconventional superconductors: Microwave conductivity shows that $κ - {(BEDT - TTF)}_{2} Cu [N {(CN)}_{2}] Br$ is a $d_{x y}$ superconductor

D. C. Cavanagh and B. J. Powell

Phys. Rev. B 100, 054505 – Published 5 August 2019

Abstract

Microwave conductivity experiments can directly measure the quasiparticle scattering rate in the superconducting state. We show that this, combined with knowledge of the Fermi surface geometry, can distinguish between closely related superconducting order parameters, e.g., $d_{x^{2} - y^{2}}$ and $d_{x y}$ superconductivity. We benchmark this method on ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ and, unsurprisingly, confirm that this is a $d_{x^{2} - y^{2}}$ superconductor. We then apply our method to $κ - {(BEDT - TTF)}_{2} Cu [N {(CN)}_{2}] Br$ , which we discover is a $d_{x y}$ superconductor.

Received 20 March 2019
Revised 8 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.054505

Physics Subject Headings (PhySH)

Electrical conductivity Penetration depth Superconducting gap Superconducting order parameter d-wave

Cuprates High-temperature superconductors Organic superconductors

Microwave techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. C. Cavanagh ^1,2,* and B. J. Powell¹

¹School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
²Department of Physics, The University of Otago, Dunedin 9054, New Zealand

^*david.cavanagh1@uqconnect.edu.au

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 100, Iss. 5 — 1 August 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Typical umklapp scattering process involving nodal quasiparticles in YBCO, assuming (a) $d_{x^{2} - y^{2}}$ pairing and (b) $d_{x y}$ pairing, in this panel we plot momenta outside of the FBZ for clarity. In (a) umklapp scattering necessarily involves particles away from the nodes, leading to an exponentially activated umklapp scattering rate. In (b) umklapp scattering is possible involving only nodal quasiparticles, leading to $τ_{u}^{- 1} \propto T^{3}$ . The activated temperature dependence of the relaxation rate is therefore sufficient to distinguish between these two gap symmetries, independent of other experiments. Dashed arrows indicate the reciprocal lattice vectors, dotted arrows are guides to the eye to show the total momentum before and after the scattering process. The Fermi surface is calculated from the single band model for YBCO [15], and the shading denotes the sign of the order parameter.
Reuse & Permissions
Figure 2
Momentum configurations for umklapp processes involving nodal quasiparticles in $κ$ -Br for (a) $d_{x^{2} - y^{2}} + s$ pairing and (b) $d_{x y}$ pairing. For $d_{x^{2} - y^{2}} + s$ pairing umklapp scattering must involve particles away from the nodes, leading to an exponentially activated umklapp scattering rate. For $d_{x y}$ pairing umklapp scattering involving only nodal quasiparticles is possible in the $c$ direction, but not the $a$ direction. Therefore at low temperatures umklapp scattering in the $c$ direction dominates leading to $τ_{u}^{- 1} \propto T^{3}$ . The activated temperature dependence of the relaxation rate is therefore sufficient to distinguish between these two gap symmetries, independent of other experiments. The gap in (b) uses the parametrization of Guterding et al. [31, 32]. The Fermi surface is calculated from the “monomer” model of $κ$ -Br [48], and the shading denotes the sign of the order parameter. Only the umklapp boundary relevant to scattering in a given direction is shown.
Reuse & Permissions
Figure 3
Comparison of the calculated quasiparticle relaxation rate for the different order parameters to experimental data for (a) YBCO [13] and (b) $κ$ -Br [36]. In both cases the experimental data are described accurately by only one of the order parameters: $d_{x^{2} - y^{2}}$ for YBCO and $d_{x y}$ for $κ$ -Br. A temperature-independent constant, resulting from residual impurity scattering, has been subtracted from each set of experimental data, equal to $5.0 \times 10^{10} s^{- 1}$ in (a) and $4.7 \times 10^{10} s^{- 1}$ in (b). In both cases, the constant term is on the order of $≲ 0.01 τ_{U}^{- 1} (T_{c})$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Umklapp scattering in unconventional superconductors: Microwave conductivity shows that $κ - {(BEDT - TTF)}_{2} Cu [N {(CN)}_{2}] Br$ is a $d_{x y}$ superconductor

D. C. Cavanagh and B. J. Powell

Phys. Rev. B 100, 054505 – Published 5 August 2019

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Umklapp scattering in unconventional superconductors: Microwave conductivity shows that κ−(BEDT−TTF)2Cu[N(CN)2]Br is a dxy superconductor

D. C. Cavanagh and B. J. Powell

Phys. Rev. B 100, 054505 – Published 5 August 2019

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Umklapp scattering in unconventional superconductors: Microwave conductivity shows that $κ - {(BEDT - TTF)}_{2} Cu [N {(CN)}_{2}] Br$ is a $d_{x y}$ superconductor